Mean-Field Calculations of Fluctuations in Nuclear Collisions

Marston, J. B.

doi:10.1103/physrevlett.54.1139

Cited by 38 publications

(51 citation statements)

References 9 publications

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“…It also underestimates width of fragment mass and charge distributions in strongly dissipative collisions [70,72,77]. Thus, to obtain multiple reaction channels or widths of one-body observables one must in principle go beyond TDHF [72,[78][79][80][81].…”

Section: Formalism a Tdhf And Dc-tdhf Approachesmentioning

confidence: 99%

Shape evolution and collective dynamics of quasifission in the time-dependent Hartree-Fock approach

2015

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Background: At energies near the Coulomb barrier, capture reactions in heavy-ion collisions result either in fusion or in quasifission. The former produces a compound nucleus in statistical equilibrium, while the second leads to a reseparation of the fragments after partial mass equilibration without formation of a compound nucleus. Extracting the compound nucleus formation probability is crucial to predict superheavy-element formation crosssections. It requires a good knowledge of the fragment angular distribution which itself depends on quantities such as moments of inertia and excitation energies which have so far been somewhat arbitrary for the quasifission contribution.Purpose: Our main goal is to utlize the time-dependent Hartee-Fock (TDHF) approach to extract ingredients of the formula used in the analysis of experimental angular distributions. These include the moment-of-inertia and temperature.Methods: We investigate the evolution of the nuclear density in TDHF calculations leading to quasifission. We study the dependence of the relevant quantities on various initial conditions of the reaction process.Results: The evolution of the moment of inertia is clearly non-trivial and depends strongly on the characteristics of the collision. The temperature rises quickly when the kinetic energy is transformed into internal excitation. Then, it rises slowly during mass transfer.Conclusions: Fully microscopic theories are useful to predict the complex evolution of quantities required in macroscopic models of quasifission.

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Section: Formalism a Tdhf And Dc-tdhf Approachesmentioning

confidence: 99%

Shape evolution and collective dynamics of quasifission in the time-dependent Hartree-Fock approach

2015

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“…(4.29) has been applied to heavy ion collisions in the special case when t = t and ρ 2 0 = ρ 0 . These computations [13][14][15], which led to a better agreement with experiment, have revealed the importance of the corrections introduced by the present method.…”

Section: Resultsmentioning

confidence: 82%

“…From the definition of R, we find 14) withρ (1) (t 0 ) = 0. Comparison of the differential equations (5.12) and (5.14), and of the associated boundary conditions, completes the proof of (5.13) and hence of the property (iii).…”

Section: Extension To Linear Responsesmentioning

confidence: 99%

“…In particular, although at its stationarity point the functional (3.2) depends on the sources both explicitly and through A(t) and D(t), only the explicit dependence contributes to the first derivative of the generating functional with respect to the ξ j (t). We have therefore at the stationarity point of (3.2) 14) where the last expression follows from (3.12). It has been shown in a similar context (see sects.…”

Section: Variational Principle For the Dynamics Of The Generating Funmentioning

confidence: 99%

“…for any value of t. By varying ρ and L we find with the above definitions [3] 14) to be solved with the boundary conditions L(∞) = 0, ρ (t 0 ) = ρ 0 . We are interested in the dependence of ϕ upon the sources ξ j (t); it will be given by (4.12) and (4.7), where the variational parameters ( , L, z, ρ)…”

Section: Application: Two-time Causal Functions and The Backward Rpamentioning

confidence: 99%

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Variational approach to multi-time correlation functions

Balian¹,

Vénéroni²

1993

Nuclear Physics B

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URL: http://www-spht.cea.fr/articles/T93/030International audienceA variational method is proposed to evaluate the generating functional $ \varphi $ which gives the multi-time correlation functions in equilibrium and non-equilibrium statistical mechanics or field theories. Its definition, $ \varphi = {\rm ln\ Tr} \ D\ A, $ involves the density operator $ D $ describing the initial state and an operator $ A $ depending on the observables of interest (in the Heisenberg picture), on the associated time-dependent sources and on the initial time. Regarded as function of this time, $ A $ is specified by a simple differential equation with the time running backward. Lagrangian multipliers are introduced to account both for this equation and for the one which characterizes $ D. $ Through this procedure $ \varphi $ is obtained as the stationary value of a functional depending on state-like and observable-like trial operators, with a complex time. Within a trial subspace, the resulting approximation optimizes both the initial state and the dynamics. The example of interacting fermions in many-body physics is worked out by restricting the trial objects to exponentials of single-particle operators. This leads to an extended mean-field approximation for the generating functional associated with any set of observables. Expansion in powers of the sources provides a variational approximation for the two-time causal or response functions. The result incorporates both the static and dynamic Hartree-Fock equations as well as the associated RPA equations. It is free of several inconsistencies occurring in the conventional mean-field approximations. ----- Les auteurs proposent une méthode variationnelle très souple pour évaluer la fonction génératrice des fonctions de corrélations d'observables arbitraires dans un système de mécanique quantique général, où l'état initial est une matrice densité arbitraire. L'un des aspects originaux est d'envisager la dépendance des quantités dans la variable temporelle où sont identifiées les représentations de Schrödinger et de Heisenberg. Les données et les équations du mouvement sont traitées comme des contraintes dans ce formalisme en introduisant des multiplicateurs de Lagrange appropriés. Les auteurs présentent à titre d'application l'exemple d'un système de fermions en interaction et trouvent des généralisations des diverses méthodes de champ moyen, statique ou dynamique (approximation de Hartree-Fock stationnaire ou dépendant du temps, méthode des phases aléatoires...). Ils montrent que leur nouvelle théorie est plus cohérente que celles envisagées jusqu'ici. \vskip 20mm \hfill{C. Itzykson

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From Light to Hyper-heavy Molecules and Neutron-Star Crusts in a Dynamical Mean-Field Approach

Simenel

2014

Clusters in Nuclei, Volume 3

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The richness of phenomena occurring in heavy-ion collisions calls for microscopic approaches where the motion of each nucleon is treated quantum mechanically. The most popular microscopic approach for low-energy collisions between atomic nuclei is the time-dependent Hartree-Fock (TDHF) theory, providing a mean-field dynamics of the system. The TDHF approach and some of its extensions are used to predict the evolution of out-of-equilibrium nuclear systems. The formation of di-nuclear systems with a structure close to molecular states is investigated. In particular, lifetimes and exit channels are described. The formation of light molecules and the dynamics of α-clustering are discussed. Di-nuclear systems formed in transfer, deep-inelastic, and quasi-fission reactions, as well as hyperheavy molecules produced in reactions between actinides are also investigated. The formation and stability of structures in neutron star crusts are finally discussed.

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Mean-Field Calculations of Fluctuations in Nuclear Collisions

Cited by 38 publications

References 9 publications

Shape evolution and collective dynamics of quasifission in the time-dependent Hartree-Fock approach

Shape evolution and collective dynamics of quasifission in the time-dependent Hartree-Fock approach

Variational approach to multi-time correlation functions

From Light to Hyper-heavy Molecules and Neutron-Star Crusts in a Dynamical Mean-Field Approach

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